拉格朗日中值定理在方程有根证明题中的应用

对微分中值定理证明方程有根的题型作了分类,分析并讨论了证明中的技巧,及证明中所采用的方法,并对不同例子进行了相应的拓展.     

2,4-二甲基吡咯-3,5-二羧酸二乙酯的合成——推荐一个大学有机化学实验

采用Knorr吡咯合成法，以乙酰乙酸乙酯和亚硝酸钠为原料，在醋酸和锌粉作用下采用“一锅法”得到2,4-二甲基吡咯-3,5-二羧酸二乙酯。本实验涉及到控温、回流、重结晶、熔点测定、红外光谱及核磁共振等实验操作和分析检测方法。该实验原料简单易得、产物收率高，结合波谱解析方法，可以培养和提高学生合成实验的能力，加强学生对杂环合成和波谱解析的理解与分析。     

Ultrathin Co3S4 Nanosheets that Synergistically Engineer Spin States and Exposed Polyhedra that Promote Water Oxidation under Neutral Conditions

Development of efficient and affordable electrocatalysts in neutral solutions is paramount importance for the renewable energy. Herein, we report that the oxygen evolution reaction (OER) performance of Co₃S₄ under neutral conditions can be enhanced by exposed octahedral planes and self‐adapted spin states in atomically thin nanosheets. A HAADF image clearly confirmed that the active octahedra with Jahn–Teller distortions were exposed exclusively. Most importantly, in the atomically thin nanosheets, the spin states of Co³⁺ in the octahedral self‐adapt from low‐spin to high‐spin states. As a result, the synergistic effect endow the Co₃S₄ nanosheets with superior OER performance, with exceptional low onset overpotentials of circa 0.31 V in neutral solutions, which is state‐of‐the‐art among inorganic non‐noble metal compounds.     

Thermal Conversion of Methane to Formaldehyde Promoted by Gold in AuNbO3+ Cluster Cations

In addition to generation of a methyl radical, formation of a formaldehyde molecule was observed in the thermal reaction of methane with AuNbO₃⁺ heteronuclear oxide cluster cations. The clusters were prepared by laser ablation and mass‐selected to react with CH₄ in an ion‐trap reactor under thermal collision conditions. The reaction was studied by mass spectrometry and DFT calculations. The latter indicated that the gold atom promotes formaldehyde formation through transformation of an Au?O bond into an Au?Nb bond during the reaction.     

EAST ������ICRF ���ߵ���ά��ų�����

The performance of the four strap ion cyclotron range of frequency (ICRF) antenna in EAST was studied by three dimensional electromagnetic code CST MWS. The coupling impedance with various frequencies, the distribution of current on straps and the power spectra for the three types of phases were calculated. The voltage breakdown and ICRF-related impurity were also studied. Simulation results show that the coupling impedance and power spectrum of the antenna design were reasonable, however, highest electric field, which is 3.61MV•m⁻¹ for (0, 0, 0, 0) toroidal phasing at the local area, exceeds the empirical value of breakdown. After the structure size was optimized, the maximum of E-field was below the breakdown value, the results also show that the high radio frequency (RF) potential was close to the antenna limiter, the RF potential along total B-field in front of Faraday screens 10mm for (0, π, π, 0) phasing was one-third of that for (0, 0, π, π) phasing.     

Robust construction of minimal surface from general initial mesh

We analyze three commonly used energy functions in solving Plateau-Mesh Problem, that is, Dirichlet, area, and the discrete mean curvature(DMC)They all possess unique advantages compared to others, but their drawbacks restrict their usages individuallyOur algorithm combines the three steps together to make full use of their featuresAt first the Dirichlet energy is optimized for faster approximation with better topologyThen the area energy is used to come close to the constrained domainFinally the DMC energy is engaged to achieve a better converging stepResults show that our method can work under a rather noisy initial mesh, which is even topologically different from the final result.     

激光能量对反钙钛矿GaCMn_3薄膜结构与物性的影响

本文采用脉冲激光沉积方法在LaAlO3(001)单晶衬底上制备了反钙钛矿GaCMn3薄膜,通过控制制备过程中脉冲激光的能量,研究了不同激光能量条件对GaCMn3薄膜结构与物理性能的影响.分别利用X射线衍射仪、原子力显微镜、超导量子干涉仪和物理性能测试系统,对所制备的薄膜的晶体结构、表面形貌和磁性、电输运性质进行了研究.结果表明,制备的样品均为具有多个晶面取向的反钙钛矿薄膜,且薄膜结构和物性明显随制备激光能量的变化而变化.当激光能量为450mJ时,制备的薄膜多晶面取向性最弱,结晶性和表面形貌最优良.实验所得的薄膜均表现出顺磁-铁磁-反铁磁相转变,然而转变过程比块材较平缓,同时薄膜的电阻率并未表现出块材中的突变特征,我们推测该现象很可能是由衬底的应力及衬底的晶格膨胀对薄膜反常晶格变化的抑制作用造成的.